Pierre Hérigone (

Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...

ized as Petrus Herigonius) (1580–1643) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...

. Of

Basque Basque may refer to: * Basques, an ethnic group of Spain and France * Basque language, their language Places * Basque Country (greater region), the homeland of the Basque people with parts in both Spain and France * Basque Country (autonomous co ...

origin, Hérigone taught in

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...

for most of his life.

Works

Only one work by Hérigone is known to exist: ''Cursus mathematicus, nova, brevi, et clara methodo demonstratus, per notas reales et universales, citra usum cujuscunque idiomatis intellectu faciles'' (published in Paris in six volumes from 1634 to 1637; second edition 1644), a compendium of

elementary mathematics Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. In the Canadian curriculum, there are six basic strands in Elementary Mathematics: Number, Algebra, Data, Spatial Sense, Finan ...

written in French and

. The work introduced a system of

mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and logical notation. It has been said that "Hérigone introduced so many new symbols in this six-volume work that some suggest that the introduction of these symbols, rather than an effective mathematics text, was his goal."

Florian Cajori Florian Cajori (February 28, 1859 – August 14 or 15, 1930) was a Swiss-American historian of mathematics. Biography Florian Cajori was born in Zillis, Switzerland, as the son of Georg Cajori and Catherine Camenisch. He attended schools first ...

has written that the work contains "a full recognition of the importance of notation and an almost reckless eagerness to introduce an exhaustive set of symbols..." Hérigone may have been the first to introduce the mathematical symbol to express an

angle In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the '' vertex'' of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles a ...

. He used both the symbol below and recorded the use of "<" as a symbol denoting " less than." He also introduced the upside-down "T" symbol (⊥) to express

perpendicularity In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can ...

In regards to the notation for exponents, Herigone wrote a, a2, a3, etc. (though the numerals were not raised, however, as they are today). Hérigone also created a number

alphabet An alphabet is a standardized set of basic written graphemes (called letters) that represent the phonemes of certain spoken languages. Not all writing systems represent language in this way; in a syllabary, each character represents a syllab ...

for remembering long numbers in which

phoneme In phonology and linguistics, a phoneme () is a unit of sound that can distinguish one word from another in a particular language. For example, in most dialects of English, with the notable exception of the West Midlands and the north-wes ...

s were assigned to different numbers, while the

vowel A vowel is a syllabic speech sound pronounced without any stricture in the vocal tract. Vowels are one of the two principal classes of speech sounds, the other being the consonant. Vowels vary in quality, in loudness and also in quantity (leng ...

s were supplied by the memorizer: 1 (t, d), 2 (n), 3 (m), 4 (r), 5 (l), 6 (j, ch, sh), 7 (c, k, g), 8 (f, v, ph), 9 (p, b), 10 (z, s). (see article Herigone's mnemonic system). In Hérigone's work, we find the earliest written examples of mathematical terms. ''Parallelipipedon'', an archaic form of '' parallelepiped'', appears in an English work dated 1570. Hérigone himself used the spelling ''parallelepipedum''.

Hérigone and the camera obscura

In the ''Cursus mathematicus'', Hérigone describes a

camera obscura A camera obscura (; ) is a darkened room with a small hole or lens at one side through which an image is projected onto a wall or table opposite the hole. ''Camera obscura'' can also refer to analogous constructions such as a box or tent in w ...

in the form of a

goblet A chalice (from Latin 'mug', borrowed from Ancient Greek () 'cup') or goblet is a footed cup intended to hold a drink. In religious practice, a chalice is often used for drinking during a ceremony or may carry a certain symbolic meaning. R ...

(Chapter 6, page 113). Hérigone did not depict his goblet, but

Johann Zahn Johann Zahn (29 March 1641, Karlstadt am Main – 27 June 1707) was the seventeenth-century German author of ''Oculus Artificialis Teledioptricus Sive Telescopium'' (Würzburg, 1685). This work contains many descriptions and diagrams, illustrati ...

would illustrate the design in his ''Oculus Artificialis Teledioptricus Sive Telescopium'' (1685). Hérigone's goblet-camera obscura, more a

novelty Novelty (derived from Latin word ''novus'' for "new") is the quality of being new, or following from that, of being striking, original or unusual. Novelty may be the shared experience of a new cultural phenomenon or the subjective perception of an ...

than anything else, was constructed in such a way that you could spy on others while taking a drink. The device's 45-degree angle mirror had a stylized opening for the lens. The goblet had a cup made of glass where images could be seen. The lid bore a magnifying lens at the to

The lens and mirror of this dinner table device for spying was situated at the base of the goblet's stem and served to project a real-time image onto the ground glass screen in the cup of the goblet.

Committee work

Hérigone served on a number of scientific committees, including one set up to determine whether Jean-Baptiste Morin (mathematician), Jean-Baptiste Morin's scheme for determining

longitude Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lette ...

from the Moon's motion was practical. Members of this committee included

Étienne Pascal Étienne Pascal (; 2 May 1588 – 24 September 1651) was a French chief tax officer and the father of Blaise Pascal. Biography Pascal was born in Clermont to Martin Pascal, the treasurer of France, and Marguerite Pascal de Mons. He had three da ...

and Claude Mydorge. He died in Paris. The crater Herigonius on the

Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

is named after him.

Notes

Sources

Biography of Pierre Herigone
*

{{DEFAULTSORT:Herigone, Pierre 1580 births 1643 deaths 17th-century French astronomers 17th-century French inventors 17th-century French mathematicians Number theorists French-Basque people